LONDON — Carmelo Anthony couldn’t miss Thursday night, filling the baskets in London with history, just as he did at Syracuse in winning the school its only national championship in 2003.

As Anthony weaved a record-setting Olympic night, Syracuse coaching legend Jim Boeheim, a Team USA assistant, just kept thinking: Why does his former college prodigy get knocked so often?

“He gets criticized for what he does, and that’s being an offensive machine,’’ Boeheim told The Post after Team USA humiliated Nigeria in a record-setting 83-point rout, 156-73. “I’m tired of reading it. He doesn’t play like LeBron James. He can pass, but he’s a scorer. He’s an offensive force. That’s what he does. He’s an offensive scorer, and internationally, he’s unguardable at the 4. You really need a 3 to guard him, but then he can take him inside.’’

Anthony finished with a mind-boggling 37 points in 14:29, the most points in U.S. Olympic team history, breaking Stephon Marbury’s single-game record of 31 from 2004. Anthony drained 10 of 12 3-pointers — setting the 3-point mark, also by smashing his fellow Brooklynite’s record of five.

After making his fifth straight trey in the third, Anthony laughed and turned up his palms as Michael Jordan used to do.

Team USA is back in action today against Lithuania, and there always is a chance Anthony will erupt again. He shot 13-of-16 overall against Nigeria and is 19-of-22 in the past two wins.

“He shot well in Syracuse, but he was best scoring and attacking inside,’’ Boeheim said. “He shot 35 percent [from 3] for me. One thing he’s done is really worked and improved his outside shooting.’’

Still, the knocks continue: Too selfish. Not a winner. Doesn’t play defense for a full game. And coach-killer.

“I talked to him when he went to New York,’’ Boeheim said. “Whether it’s a good team or not, they will blame you if they lose. Last year, they didn’t have the team to win against Miami. They didn’t have a point guard. They didn’t shoot it at the 2. They had many deficiencies. No NBA player can win a championship alone. LeBron James tried it in Cleveland and couldn’t do it.

“And Melo knows it will be on him this year,’’ Boeheim added. “He’s doing everything he can do to get ready for the season, and this Olympics is great for him because he’s going to be in great shape for training camp.’’

Boeheim and former Knicks coach Mike D’Antoni have been on the same Olympic staff for six years. D’Antoni’s falling-out with Anthony is a touchy subject because Boeheim is friends with both of them. The two have gotten along fine since the Olympic team gathered in Vegas on July 5, but wounds are still healing.

“The first year it went well, but then the whole thing exploded,’’ Boeheim said. “I just don’t think it was a good fit. It didn’t fit well when Melo came back with [Jeremy] Lin. They couldn’t fit it back together because Mike went in a different direction.’’

Boeheim gets MSG Network on his Syracuse cable system, and says he watches virtually every single Knicks game since Anthony came aboard. He’s still worried about the team’s fortunes, no matter how spectacular Anthony is.

“The bigger question is: Can Amar’e [Stoudemire] and Carmelo fit together going forward,’’ Boeheim said. “Because J-Kidd will get the guys the ball. It’s how they play off each other. There’s still a lot of questions marks. Will the point guard situation be OK with Kidd, Felton and Amar’e’s body holding up?’’

If the Knicks underachieve, Boeheim doubts it will be due to Anthony.

“He makes winning basketball plays,’’ Boeheim said. “I know he can win. He won for me, and I know what’s he’s capable of.’’

Coach Mike Krzyzewski gave team off yesterday after their record-setting showing, choosing to hold a meeting and stage a walk-through in the team hotel.

“I took home the box score to frame it,’’ Boeheim said. “No one’s seen anything quite like it or will again. Forty-nine points in the first quarter — and it’s 10 minutes.’’